e.
Explain what a “particle in a box” is.
It is a model that can be used to solve the Schrodinger equation. It is used to describe a particle
that is free to move within a box. The box is confined because of the areas outside are infinite
potentials. The particle is not allowed to be in the areas of infinite potential.

2. Answer the following questions.
a. Describe the experimental results that led to quantum mechanics.
The experiment that led to quantum mechanics is
Schrödinger’s
cat. The experiment was to put a
cat in a box for an hour. The cat could be alive, or it could be dead, but that would be unknown
until the box is open. So, the cat is equally alive and dead while the box is closed. This related to
a particle having a wavelength. For something to have a wavelength it must occupy multiple
positions at the same time. The wavelength of an object limited to a small space cannot be
perfectly defined so it exists in multiple different wavelengths at the same time.
b. Describe
how to get the measured value (e.g. temperature
or
momentum) from
a
wavefunction.
To get an expect or average value of temperature we integrate the complex conjugate of
wavefunction, the temperature operator and wavefunction over space.
c. Explain what atomic units are.
SI units are used to describe things that we can see and bigger. An atom, nucleus, and electrons
are so much smaller. They need to have their own units. To get atomic units from SI units
normalize all the units so that everything is equals to 1.
d. Explain why an
electron around a proton nucleus doesn’t collapse into the nucleus.
An electron in an atom spreads out according to its energy. The states with more energy are more
spread out. All electron states overlap with the nucleus. Electrons are partially in the nucleus.

3.If

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- Summer '20